Thursday, October 19, 2017

Introduction

A number of years ago, Dr Ugo Bardi published a very thought-provoking essay about the possibility of a universal mining machine (which I’ll refer to as “Bardi’s machine” from now on). Such a machine can take common dirt, melt it down, atomize it, and separate it into its elements, each in its own little pile. This would allow us to extract valuable elements from common dirt. It would also prevent us from ever running out any any elements, as I'll explain below.

Common dirt contains small amounts of all naturally occurring elements. You could dig up a cubic meter of dirt from behind your house, and it would contain trace amounts of every element which occurs naturally. If we atomized common dirt, using Bardi's machine, we would obtain all elements from any piece of earth fed into it. As a result, we would never absolutely "run out" of any element until we had exhausted all dirt on this planet.

Furthermore, the amount of rare elements available to us would be massive and practically inexhaustible. More than 99.9% of the rare elements (such as copper) exist as very low concentration deposits. The overwhelming majority of rare elements are found as an atom here, an atom there, spread out thinly throughout the earth's crust. If we could mine the low-concentration deposits, then we would increase the total supply of rare elements by more than a factor of 1,000x.

What's more, we would no longer be "running out" of rare elements at any rate. Once we began mining common dirt, the amount of all elements available to us would be constant, and would not diminish over any time period. When we throw away old smart phones, or we build structures that rust away, they would just return to being common dirt (eventually) and could easily be re-mined. As a result, the amount of materials available to us would not diminish over time.

Presumably, we will eventually be forced to use Bardi's machine at some point. If we continue mining and dispersing the concentrated deposits of rare elements, as we are doing, we will eventually exhaust all of them. At some point, far in the distant future, we will have exhausted all concentrated copper deposits, all the concentrated rare earth deposits, and so on. At that point, only common dirt will remain. If we wish to continue mining the rare elements at that point, we'd need to use something like Bardi's machine.

The problem with mining common dirt is that it takes so much energy to do so. Lower concentrations of elements require higher amounts of energy to mine them. The lower the concentration, the higher the energy requirement. For example, it takes 10 times as much energy to mine an ore which is only 1/10th the concentration. The problem is, the concentration of rare elements is extremely low within common dirt. As a result, it would be energetically extremely expensive to obtain any particular rare element from common dirt. From Bardi’s article:

"Consider copper, again, as an example. Copper is present at concentrations of about 25 ppm in the upper crust (Wikipedia 2007). To extract copper from the undifferentiated crust, we would need to break down rock at the atomic level providing an amount of energy comparable to the energy of formation of the rock. On the average, we can take it as something of the order of 10 MJ/kg. From these data, we can estimate about 400 GJ/kg for the energy of extraction. Now, if we wanted to keep producing 15 million tons of copper per year, as we do nowadays, by extracting it from common rock, this calculation says that we would have to spend 20 times the current worldwide production of primary energy."

That is a valid point. It seems to rule out the possibility of mining undifferentiated crust.

However, one of the commenters for that article pointed out that mining undifferentiated crust would allow us to obtain all the elements at once, not just copper, for the same expenditure of energy. In other words, that expenditure of 400 GJ would yield not just 1 kg of copper, but many kilograms of many other elements also.

Bardi wisely made a concession to that point. In his subsequent book, he calculates the energy expenditure of mining undifferentiated crust while obtaining many uncommon elements thereby.

However, I wish to continue with the commenter’s line of thinking. I wish to explore the possibility of mining undifferentiated crust (dirt) and using all the elements obtained thereby, including the common elements such as iron, aluminum, silicon, oxygen, and so on. That is the purpose of this article: to explore the energetic effects of mining undifferentiated crust and using all the material obtained thereby, or at least using as much of that material as possible.

Can we mine undifferentiated crust?

If we started mining undifferentiated crust, using Bardi’s machine, then the elements emitted from it would not correspond to our needs for them. For example, almost 80% of the material emissions from Bardi’s machine would consist of silicon, oxygen, sodium, potassium, and magnesium, which only could be used for making glass, at least in those quantities. Another 18% or so of the material emissions would be common metals such as aluminum, iron (for steel), titanium, and so on. Less than 1% would be the “uncommon elements” such as copper, nickel, rare earths, and so on. We must use the elements in precisely those proportions if we wish to avoid throwing away any elements emitted from Bardi’s machine.

It’s necessary to avoid throwing away materials, because that’s what would determine how much energy would be required for Bardi’s machine, per kilogram of materials mined. If we used everything emitted from Bardi’s machine, in the proportions in which they were emitted, then the amount of energy used for mining undifferentiated crust would be 10 MJ/kg, as per Bardi’s quotation above, which is a modest amount of energy and is similar to what we use for mining today. If, on the other hand, we mine only copper from undifferentiated crust, and throw everything else away, then the energy expenditure is 400 GJ/kg, which is 40,000 times higher.

Since we wish to avoid throwing away material, we must align our mining of undifferentiated crust with our usage of materials. Presumably, only a fraction of all mining could be done using Bardi’s machines. Some of the common elements (like aluminum and iron) would still be mined using traditional methods, so only a fraction of our mining would use Bardi’s machines. That fraction must be low enough that no materials are emitted from Bardi’s machine in greater quantities than are used by that civilization. In that manner, Bardi’s machines would displace the energy which otherwise would have been used to obtain materials for glass, steel, and so on, using traditional mining methods. We would get the common elements “for free” from Bardi’s machines, as a side effect of trying to obtain the rare ones, which would reduce the energy expenditure for mining elsewhere in the economy. As a result, the net effect of using Bardi’s machines would not increase the energy requirements for mining as a whole, at least not by very much. The advantage of using Bardi’s machine is that it would also emit small quantities of all the uncommon elements, so we would never run out of them over any time scale.

Let’s suppose that civilization has exhausted all ores and all concentrated deposits, of all rare elements, everywhere. All that remains is undifferentiated crust for uncommon elements. Also assume that civilization wishes to use Bardi’s machines as much as possible to obtain uncommon elements from that point forward. We’ll assume the civilization uses the same proportions of common elements (such as silicon, iron, and so on) as we use today.

In which case, Bardi’s machines could be used to mine all the materials for all glass produced by that civilization. Glass would be the material which was relatively most over-supplied from Bardi’s machines (almost 80% of the material emitted could only be used for making glass). As a result, if there was enough demand for all that glass from Bardi’s machines, then there would also be enough demand for all the iron, aluminum, calcium (for cement), and so on. Little material would be thrown away. All other glassmaking operations in civilization could cease, thereby saving the energy that had been expended on it. Also, some of the mining for bauxite, iron, and so on, would also be displaced by Bardi’s machines. The amount of energy used by Bardi’s machines would be on the order of 10 MJ/kg, which is not higher than civilization was already expending upon glass, aluminum, and so on.

It would be possible to make glass directly from the output of Bardi’s machines, by mixing together the necessary elements while they were still molten, and cooling the result quickly enough that glass is formed. This would displace the amount of energy used for glassmaking elsewhere in the economy, which is on the order of 15 MJ/kg of glass. Of course, we would also make some steel and some aluminum from the output of Bardi’s machines.

This strategy would reduce the amount of energy required for mining undifferentiated crust. The amount of energy for mining altogether would not be much higher than today. Furthermore, we would get all of the elements which occur in the Earth’s crust, as long as mining continued.

Elemental Scarcity

As a result, we could use Bardi’s machines to a limited degree, and could obtain all elements indefinitely, without ever increasing the energy we use for mining. We would just have to limit the use of Bardi's machines so that they don't produce much more of any elements than were otherwise mined.

The problem is, the amounts of uncommon elements would be emitted in fairly limited quantities. We’d never run out of uncommon elements, but the amounts produced per year of copper, nickel, and so on, would be fairly limited, assuming we don’t wish to “throw away” anything, and thereby increase the amount of energy devoted to mining intolerably.

At present, global civilization produces about 70 million tonnes of glass per year. If all that glass were produced from materials from Bardi’s machines, then the following amounts of rare elements would also be obtained:

Copper (70 megatonnes * 70ppm) = 4,900 tonnes/year

Nickel (70 megatonnes * 90ppm) = 6,300 tonnes/year

Lithium = ~1,800 tonnes/year

"Rare Earth" elements = ~20,000 tonnes/year

As a result, we would mine 0.7 grams of copper per person per year, and also 0.9 grams of nickel, worldwide, and similar or smaller amounts of all the other uncommon elements per person each year. Doing so would never require more energy than is expended on mining now. We could mine those rare elements, in those amounts, from undifferentiated crust until the sun explodes. We would never run out of them, and would never expend any more energy on mining than we do now.

Conclusion

As a result, our civilization could always have enough of the uncommon elements for things like smart phones, flat screen televisions, computer chips, and so on. Many of those devices use less than one gram of uncommon elements, per device. We could always mine enough materials for those purposes, even after billions of years.

We would also have enough uncommon elements for "massive" uses of them, such as electric cars, as long as we enforce high rates of recycling. For example, we would have enough lithium for electric cars indefinitely, provided that the batteries are sealed from the environment and the recycling rate is 99% or higher. If we assume that an electric vehicle has 30 kg of lithium in its batteries, the batteries are sealed from the environment, the car lasts 20 years, and 99.9% of the lithium in electric cars is recycled, then an average electric vehicle would require a net of 1.5 grams of lithium per year to be mined. That amount is on the order of what would be emitted from Bardi's machines, with no additional expenditure of energy. As a result, we would have enough lithium (and other uncommon elements) for "bulk" uses, indefinitely, as long as we enforce high rates of recycling.

We would not, however, have enough rare elements for “bulk” usages that are just thrown away. Some day, we will not have enough uncommon elements to allow people to throw away larger than single-digit gram quantities of rare elements per year. At some point, careful recycling will be required for devices (such as electric cars) which use large quantities of uncommon elements.

A few caveats are necessary here. It's possible that we won't have enough lithium in the future to build additional new electric vehicles. We would have enough lithium to sustain the peak number of electric cars indefinitely, but not enough to build additional new electric cars. Also, it is quite possible that we will simply substitute other elements when rare ones become scarcer, in which case, we would not pursue the diffuse deposits for those elements.

However, we will never "run out" of any element over any time period. The conclusion is that we can mine undifferentiated crust, in limited amounts. It is energetically feasible to do so. As a result, we will never run out of any element over any time period. We may have much lower extraction of some elements, far in the future, but extraction will never be zero for any important element. All uncommon elements will always be available, at tolerable energy expense.

NOTE: I made two changes to this article the day after it was published, as explained in the comments below. I also added the "caveats" paragraph shortly after this article was first published.

Monday, September 18, 2017

(Note: this is a draft. I will update it if any relevant objections are made).

Introduction

In an excellent blog post, Dr Tom Murphy examined whether it would be possible to power the entire USA using a combination of renewables and lead-acid batteries. He found that it would not be possible, because there is nowhere near enough lead in the earth's crust to make enough lead-acid batteries to compensate for the intermittency of renewables. Renewables occasionally don't produce power for 7 days in a row (during prolonged wind lulls, for example). As a result, it would be necessary to build enough lead acid batteries to power the country for 7 days to prevent the lights going off during those periods. However, the amount of lead in the earth's crust is not sufficient even to power just the USA for 1/3rd that long, to say nothing of the rest of the world. As a result, lead-acid batteries cannot compensate for the intermittency of renewables on a nationwide scale.

However, lead-acid batteries are not the only storage option available. We should investigate whether there are other storage options that have sufficient materials, not just whether lead-acid batteries have sufficient materials.

In this article I’ll investigate some other energy storage options. I'll try to determine if those options would be sufficient to power the entire USA during wind lulls. In all cases, I will assume that society needs 7 days of energy storage (or 336 billion kWh for the USA, as per Dr Murphy’s article) to prevent the lights from going out during occasional prolonged lulls in wind power.

Molten Silicon

First I will examine the possibility of using molten silicon as an energy storage medium. Molten silicon would be stored in insulated tanks, and heated up whenever the wind is blowing. When the wind isn’t blowing, hot air is drawn over the molten silicon and used to drive a turbine. The silicon doesn’t actually change temperature; instead it changes phase from solid to liquid when heat is added, and back from liquid to solid when heat is taken out, so the temperature remains constant at 1414 degrees C. This technology is already being pursued by a startup; see here.

Let’s find out if there is enough silicon in the earth’s crust to provide energy storage for the USA for 7 days. We’ll start by calculating how much silicon metal would be required. Murphy’s article says that we’d need 336 billion kWh to power the entire country for 7 days. Silicon has a latent heat of melting of 1.926 MJ/kg[2], which is equivalent to 0.535 kWh/kg, or 0.278 kWh/kg after subtracting waste heat losses (discussed further below). As a result, we would need 1.2 billion tonnes of silicon (336 billion / 0.278), which is a cube of silicon that’s 0.78 kilometers on a side (at 2.5 g/cm^3 [3]). Silicon is the primary ingredient of dirt, so we could gather a cube of silicon that’s 0.78 kilometers on a side from within a 10 kilometer radius around my house. That would be enough silicon to power the entire USA for 7 days. Furthermore, the silicon is not being “used up” at any rate, but could be re-melted, over and over again, for millions of cycles, with no degradation.

Of course, we’d also need gas turbines, in order to convert the heat back into electricity. However, gas turbines have already been scaled up and already provide much of the electricity generation for the world. Those are natural gas turbines, not hot air turbines, but their construction would be similar. I presume we can continue building gas turbines on a wide scale.

As a result, it is clear that we have vastly more silicon than we need to meet our energy storage requirements for the entire USA for all purposes, and can also build the requisite turbines on a wide scale.

Power-to-methane

Power-to-methane relies upon electrolyzing water to obtain hydrogen gas, then converting that hydrogen gas to methane using the Sabatier process. When the wind is blowing, methane gas is created. When the wind isn't blowing, that gas is converted back into electricity using existing natural gas turbines.

There is enough carbon in the Earth’s atmosphere to create the needed methane gas. We've been burning fossil fuels for more than a century now, so there is obviously enough carbon in the atmosphere to make a 7-day inventory of methane gas. Remember that carbon is not being “used up” during this process of synthesizing gas and burning it. This storage scheme is a closed cycle, in which carbon is taken from the atmosphere (actually, probably absorbed from the atmosphere into the oceans and then taken from there) and then re-released to the atmosphere. As a result, the maximum amount of carbon we would ever need is a 7 day inventory of methane, which obviously is a small fraction of the carbon we have emitted into the atmosphere over the last century.

There is also the question of how we could store 7 days worth of methane gas. However, that gas could be injected into the existing natural gas distribution network, which already is large enough to store months of gas. For example, California (where I live) can store 2 months of gas in the existing gas distribution network.[5]

It is clear that power-to-methane could be scaled up to provide 7 days of storage when the wind isn’t blowing.

Compressed Air Energy Storage

Compressed air energy storage relies upon compressing air when the wind is blowing. The compressed air can be stored in naturally-occurring underground caverns. When the wind stops blowing, the compressed air is released which powers a turbine and generates electricity.

There are enough caverns underground worldwide to hold the compressed air. The world is scattered with underground salt domes, salt caverns, porous rock formations, and aquifers. Here is a map of salt formations in Europe, for example[4].

There is one formation underneath Poland and Germany, for example, that appears to be 1,000 km long and 100 km wide. If it's 2 km deep, then it has a total volume of 200,000 km^3. Compressed air stores approximately 4 kWh/m^3 which is 800,000 billion kWh for the entire formation, whereas we need only 336 billion kWh for the USA according to Murphy's article. Obviously, it wouldn't be possible to convert an entire large underground salt region to a single compressed energy store. Still, if we could use even 0.1% of it, then we'd have more than enough energy storage for that region.

It is also possible to store compressed air in above-ground steel tanks in the regions which do not have suitable geography for underground storage.

Conclusions

There are already many solutions for storing 7 days worth of electricity. Those solutions are fairly low-tech and do not rely upon any technological breakthroughs. Furthermore, they could all be scaled up and do not face any material constraints.

The only objection to the low-tech storage mechanisms listed above is that they have fairly low round-trip energy efficiency. For example, molten silicon storage relies upon heating silicon to 1414 degrees centigrade to power a turbine, which implies a round-trip efficiency of approximately 50%. This means that approximately half the energy placed into storage would be lost as waste heat. Power-to-gas would probably be somewhat less efficient, at 40% or so (60% lost as waste heat). Compressed air could be somewhat higher, at 60-70%. In all cases, however, there would be considerable round-trip energy losses.

However, that drawback is not as important as it would seem. Those energy losses are incurred only part of the time, because most renewable electricity is delivered directly to the grid without ever being placed into storage. As a result, storage losses would constitute only a fairly small fraction of the total electricity generated. For example, if solar panels could provide enough electricity to meet 40% of electricity demand directly, without storage, then only 60% of electricity would need to be drawn from storage. In which case, we would need to overbuild solar panels by only 60% (not 100%) to compensate for storage losses with 50% efficient storage (0.40 electricity delivered directly, 0.60 to storage, and 0.60 to waste heat, which implies 1.60/1.00, which is 60% overbuilding). Waste heat losses would constitute only 37.5% (0.6/1.6) of all energy obtained from solar panels, not 50%.

As a result, the round-trip losses from energy storage would be less important, because those losses are incurred only part of the time. This is quite different from waste heat losses from coal power plants, for example. Coal power plants lose 65% of their energy as waste heat, 100% of the time. On the other hand, the round-trip losses from energy storage from renewables are only occasional, and so would represent a fairly small fraction of all electricity generated.

As a result, it is clearly possible to build a “nation-sized” energy storage mechanism with tolerable energy losses and at reasonable expense. We do not face material constraints on energy storage. No technological breakthroughs are required. We could build an energy storage system that would provide continuous, dispatchable power at all times from renewable sources.

One more thing. There are also newer electricity storage mechanisms being developed. For example there are new flow batteries being developed which use abundant materials (such as the iron flow battery described here, or the organic flow battery described here). Those flow batteries would have higher round-trip efficiency (like 70% or more) and could store large amounts of energy at the same time. If higher round-trip efficiencies could be achieved, then less overbuilding would be required. Overbuilding is unfortunate, and we should try to reduce it. However, even if those new flow battery technologies never reach commercialization, we still have other, lower-tech options which are perfectly workable and which impose modest energy losses relative to all electricity generated.

Thursday, September 14, 2017

The United States has 283 years of coal remaining, at present rates of usage, according to the EIA[1]. China, Russia, and Australia have similarly huge amounts.

However, that figure of 283 years remaining is for present rates of usage. If coal usage declines, then the "hubbert curve" of remaining coal is flattened and pushed further out to the right. For example, if we were using only half the amount of coal per year as we do now, then we would have 566 years of coal remaining, not 283 years. Every reduction in coal usage will extend the amount of time remaining until depletion.

Coal usage has been declining fairly rapidly in the United States, for the last 5 years or so, because renewables and gas are so much cheaper now. Coal plants are being shuttered because coal is relatively more expensive now. In fact, coal usage is down 28% in the United States over the last 5 years, because so many coal plants have been shuttered[2]. As a result, the date of coal depletion is being pushed far out into the future. Since coal usage is down 28% already, the remaining time until coal is depleted has increased from 283 years to 388 years (= 283 / 0.72 - 5). In other words, we have “gained” 105 years of coal during the last 5 years.

This trend looks set to continue. New turbines are being developed ("supercritical CO2 turbines") to replace the old steam turbines in coal power plants. Those new turbines are 50% efficient instead of 33%, which pushes back the date of depletion another 262 years ( =393 * (0.5/0.33) ). Any further encroachment of renewables would push back the date of depletion even further, and could easily result in millennia of coal before it runs out. For example, if coal plants are gradually replaced by wind turbines during the next few decades, until coal is used only for steelmaking and also during the time when the wind isn't blowing, then coal usage could decline by more than 50%, which would result in 1,190 years total until the coal runs out (= 595/0.5). That figure is without any electricity storage technology at all for when the wind isn't blowing. Coal could still be used for electricity generation when the wind isn't blowing, but we'd still have enough coal for 1,190 years.

Of course, there are several trends happening in the opposite direction also, which could push toward increased use of coal. First, the United States looks like it will phase out nuclear power over the next several decades, and some of that lost generation may be replaced by coal. Second, south Asia is growing quickly and will increase its usage of coal. However, both of those trends are temporary. Coal usage may bounce up and down, but in the long run, it is probably headed way downwards, which implies that remaining reserves will last far longer than reserve figures suggest.

Of course, it is possible that further technological developments will occur during the next few centuries, in which case the date of depletion for coal will be pushed even further outward. If flow batteries are commercialized, for example, then coal may not be needed for electricity generation at all. If new steel-making technologies continue to progress, then coal wouldn't be needed for that purpose either.

Our civilization has at least centuries to develop technologies such as flow batteries and alternative steel-making technologies. If those technologies are developed and commercialized in the next few centuries, then the remaining coal would be left in the ground as useless.

Technology is rapidly outpacing depletion. This time to depletion for coal keeps getting further and further away, and fairly rapidly. If this trend continues for long, then coal will never run out.

[1] https://www.eia.gov/energyexplained/index.cfm?page=coal_reserves

[2] https://www.eia.gov/coal/production/quarterly/pdf/t1p01p1.pdf

*NOTE: This post was revised several times during the 24 hours after its initial publication. I also updated this article on Sept 21 to use a more realistic example of how much electricity could be generated from renewables without storage.